Electronic Theses and Dissertations
Date of Award
Doctor of Philosophy
Pseudo-random numbers (PRNs) are the basis for almost any statistical simulation and thisdepends largely on the quality of the pseudo-random number generator(PRNG) used. In this study, we used some results from number theory to propose an efficient method to accelerate the computer search of super-order maximum period multiple recursive generators (MRGs). We conduct efficient computer searches and successfully found prime modulus p, and the associated order k; (k = 40751; k = 50551; k = 50873) such that R(k; p) is a prime. Using these values of ks, together with the generalized Mersenne prime algorithm, we found and listed many efficient, portable, and super-order MRGs with period lengths of approximately 10e 380278.1;10e 471730.6; and 10e 474729.3. In other words, using the generalized Mersenne prime algorithm, we extended some known results of some efficient, portable, and maximum period MRGs. In particular, the DX/DL/DS/DT large order generators are extended to super-order generators.For r k, super-order generators in MRG(k,p) are quite close to an ideal generator. Forr > k; the r-dimensional points lie on a relatively small family of equidistant parallel hyperplanesin a high dimensional space. The goodness of these generators depend largely on the distance between these hyperplanes. For LCGs, MRGs, and other generators with lattice structures, the spectral test, which is a theoretical test that gives some measure of uniformity greater than the order k of the MRG, is the most perfect figure of merit. A drawback of the spectral test is its computational complexity. We used a simple and intuitive method that employs the LLL algorithm, to calculate the spectral test. Using this method, we extended the search for better DX-k-s-t farther than the known value of k = 25013: In particular, we searched and listed better super-order DX-k-s-t generators for k = 40751; k = 50551, and k = 50873.Finally, we examined, another special class of MRGs with many nonzero terms known as the DW-k generator. The DW-k generators iteration can be implemented efficiently and in parallel, using a k-th order matrix congruential generator (MCG) sharing the same characteristic polynomial. We extended some known results, by searching for super-order DW-k generators, using our super large k values that we obtained in this study. Using extensive computer searches, we found and listed some super-order, maximum period DW(k; A, B, C, p = 2e 31 - v) generators.
Dissertation or thesis originally submitted to ProQuest
Pasiah, Kenneth Bobvah, "EFFICIENT COMPUTER SEARCH FOR MULTIPLE RECURSIVE GENERATORS" (2021). Electronic Theses and Dissertations. 2942.
Available for download on Saturday, May 25, 2024
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